An essential feature of a partial differential equation operator that models wave propagation is whether it admits solutions that will amplify or damp with time as waves propagate in space. In some physical processes, such as in liquid fuel atomizers [1]}, [2]}, [3]}, instabilities are necessary to enable the flow to break into droplets, and in other cases turbulence is used to facilitate mixing [4]}. In many processes, however, stability of wave-like disturbances is not only desired, it is required, such as in thin film coating used to manufacture printed electronics and liquid crystal display screens [5]}, [6]}.
Although the latter processes are governed by the nonlinear equations of fluid dynamics, it is standard to linearize about steady operating conditions; coating processes are run with tight constraints on the uniformity of the product, and thus linearized equations are often sufficient to predict the effect of process disturbances [7]}.
